Panaretos, John (1983): On Moran's Property of the Poisson Distribution. Published in: Biometrical Journal , Vol. Vol.25, No. 1 (1983): pp. 6976.

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Abstract
Two interesting results encountered in the literature concerning the Poisson and the negative binomial distributions are due to MORAN (1952) and PATIL & SESHADRI (1964), respectively.
MORAN's result provided a fundamental property of the Poisson distribution. Roughly speaking, he has shown that if Y, Z are independent, nonnegative, integervalued random variables with X=Y  Z then, under some mild restrictions, the conditional distribution of Y  X is binomial if and only if Y, Z are Poisson random variables.
Motivated by MORAN's result PATIL & SESHADRI obtained a general characterization. A special case of this characterization suggests that, with conditions similar to those imposed by MORAN, Y  X is negative hypergeometric if and only if Y, Z are negative binomials.
In this paper we examine the results of MORAN and PATIL & SESHADRI in the case where the conditional distribution of Y  X is truncated at an arbitrary point k1 (k=1, 2, …). In fact we attempt to answer the question as to whether MORAN's property of the Poisson distribution, and subsequently PATIL & SESHADRI's property of the negative binomial distribution, can be extended, in one form or another, to the case where Y  X is binomial truncated at k1 and negative hypergeometric truncated at k1 respectively
Item Type:  MPRA Paper 

Original Title:  On Moran's Property of the Poisson Distribution 
Language:  English 
Keywords:  Poisson Distribution, Binomial Distribution, Negative Binomial Distribution, Negative Hypergeometric Distribution, Moran's Theorem, Patil & Seshadri's Theorem 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General 
Item ID:  6231 
Depositing User:  J Panaretos 
Date Deposited:  12. Dec 2007 16:20 
Last Modified:  17. Feb 2013 21:31 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/6231 